1 Answer
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The stock messaging app will automatically save a draft message when you tap on the back button while composing the message, but the recipient field has to be filled. Without a recipient it will give a warning that the message will be deleted.

There are a lot of good alternatives. I have no experience with them myself (I'm using the stock app) but a lot of people seem to like Handcent, GO SMS Pro or ChompSMS. Just search the Internet for reviews.